Arduino Uno R3: This is the right arduino, a nifty little Italian-made board powered by USB with useful lights on the board.
An assortment of LEDs. These are nice because you get resistors with them and it is easy to figure out the voltage drop depending on the LED colors.
BB400 Solderless Plug-in Breadboard: This breadboard accepts 21-28 ga solid copper wire ends and has a power strip for workbenching your ideas.
I am having fun with these things. Another thing that is good to get are small servos, but I haven't done that yet. If you browse around Amazon you can find kits like this one from SparkFun - I bought that one for Sarah as a Christmas present. That kit was for exploration; there are other kits that are basically 'build this'. They are marked up cost-wise so if you have some idea what you want to do, piecemeal is better.